differentiate with respect to t where t is real $\displaystyle \frac{w+t}{|w+t|^2}$ where w is a constant complex number. I get $\displaystyle \frac{|z+t|^2-2(z+t)^2}{|z+t|^4}$ but that is the wrong answer in my book. Thanks
differentiate with respect to t where t is real $\displaystyle \frac{w+t}{|w+t|^2}$ where w is a constant complex number. I get $\displaystyle \frac{|z+t|^2-2(z+t)^2}{|z+t|^4}$ but that is the wrong answer in my book. Thanks
Note that $\displaystyle | w + t |^2 = (w + t)^2$ is always positive. Thus
$\displaystyle \frac{w + t}{ |w + t| ^2 } = \frac{w + t}{(w + t)^2}$
differentiate with respect to t where t is real $\displaystyle \frac{w+t}{|w+t|^2}$ where w is a constant complex number. I get $\displaystyle \frac{|z+t|^2-2(z+t)^2}{|z+t|^4}$ but that is the wrong answer in my book. Thanks
Recall that $\displaystyle |z|^2=z\cdot\overline{z}$ and because $\displaystyle t$ is real then $\displaystyle \overline{t}=t.$